ILASS 2008Sep. 8-10,2008, Como Lake, Italy

VALIDATION OF A CAVITATION AND TURBULENCE INDUCED MODEL FORTHE PRIMARY BREAKUP OF DIESEL JETS

Oscar J. Soriano1∗, Martin Sommerfeld2, Axel Burkhardt1

1Diesel Systems, Hydraulic Simulation, Continental Automotive GmbH, Regensburg, Germany2Dept. of Process Engineering, Martin-Luther University Halle-Wittenberg,

Haale (Saale), Germany

ABSTRACTIn this paper, the performance of an energy based CFD model for the primary breakup of high-pressureDiesel jets is presented. This version of the model was modified and further developed for different turbulentand cavitating flow conditions experimentally found inside the injection hole. A detailed spatial and temporalresolution of the cavitating flow in the hole is used by the model to deliver three dimensional sprays, providingall the starting conditions for the calculation of the secondary breakup of the Diesel spray by means of aLagrangian approach. The characteristic feature of the model is the variable size and velocity distributionof the primary droplets as a function of the available breakup energy. Other main advantage of the model isthe direct calculation of the droplet size distribution and spray angle on the basis of the flow properties, sothat empirical correlations or measurement data are not needed as input for the calculations. The two-fluidEulerian simulation for the cavitating flow inside the nozzle is followed by an Eulerian / Lagrangian approachoutside the nozzle, using the Ansys-CFX CFD code for both stages of the process. Measurements carried outin the test facilities of the Continental Automotive GmbH in Regensburg for high pressure Diesel jets weretaken to compare with the simulations, offering satisfactory performance.

INTRODUCTION

Combustion in a direct injection engine is strongly con-trolled by the details of the atomized fuel spray produced bythe nozzle in the injector, so that an understanding of thishigh-pressure sprays is central to the goal of optimizing fuelconsumption in the development of new engines. Not only newdeveloped experimental techniques can help reach this goal,but also computational methods show great potential for thecharacterization of these sprays.The fundamental mechanisms of atomization have been underextensive experimental and theoretical study for many years[13, 6, 7]. Today it is accepted, that the breakup of liquid jetsunder high-pressure injection conditions can be divided in twosub-processes depending on the origin of the driving physicalphenomena: primary and secondary breakup [3, 14]. In the caseof primary breakup it is assumed that the main mechanismsthat lead to the first breakup of the coherent liquid column intobig liquid drops and ligaments can be found inside the injectionnozzle. The most cited mechanisms found in the literature arecavitation and turbulence [5, 3, 6]. These are caused by the bigpressure differences (up to 2000 bar) and the tiny geometricaldimensions of the nozzle (D = 150µm), which lead to veryhigh velocities and low static pressures, locally under saturationpressure of Diesel. Cavitation structures develop becauseof the drop of static pressure inside the nozzle: the strongacceleration of the liquid at the inlet of the injection holestogether with an additional radial pressure gradient caused bythe strong curvature of the streamlines lead to a pressure fall

∗Corresponding Author

below vapour pressure. The cavitation structures implode whenentering the chamber because of the high ambient pressure.This energy contributes to the primary breakup and results inthe formation of big droplets or fluid ligaments and also inspray divergence. Other cavitation structures implode inside theinjection hole, increasing the turbulence level and promotingthe spray disintegration into big droplets. Different authorshave tried to describe the influence of turbulence and cavitationon the primary breakup [2, 11, 3, 17]. The further breakupof the primary drops and ligaments due to the aerodynamicalinteraction with the surrounding gas outside the nozzle isknown as secondary breakup.For the mathematical description of the spray and nozzle flowtwo approaches are used: the homogeneous (Euler/Euler)and the inhomogeneous (Euler/Lagrange) approach. Theinhomogeneous approach does allow mass, momentum andenergy exchange between the droplets and the gas phase, whichis indispensable for Diesel spray calculations. Due to the easierimplementation of the physical models and the robustness ofthe mathematical approach, a stochastic Lagrangian descriptionof the Diesel spray is widely used in the literature, both for thesecondary and primary breakup. According to this method-ology, all processes, which cannot be resolved deterministicon a parcel level, are solved with a Monte-Carlo-simulation.This approach is in the case of secondary breakup extensivelyaccepted, whereas for the primary some authors consider thehomogeneous approach to be more efficient [18]. Regardingthe nozzle flow simulations, almost in every literature referencethe homogeneous approach is used, assuming the same velocityand pressure for both Diesel fuel and vapour.While many models dealing with the secondary breakup can be

Paper ID ILASS08-1-13

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found in the open literature (listed in [3]), very few have beendeveloped to account for the important effects of the nozzleflow on the primary breakup. In the last few years a greateffort is being made trying to describe the primary breakup,not without considerable difficulties. One of the main reasonsfor this is the different mathematical description of the liquidfuel inside and outside the injection nozzle, as explained above,that leads to a two-step simulation process of the fuel injection.Since the primary breakup of the liquid begins inside the nozzlebut ends outside, the modelling of the breakup comprehendsnot only the acting physical processes, but also the change ofmathematical approach.

SPECIFIC OBJECTIVES AND SIMULATION AP-PROACH

The objective of this paper is the validation of the perfor-mance of a cavitation and turbulence-induced break-up spraymodel by means of optical measurements of the penetration andangle of the injected spray. The initial turbulent and cavitatingconditions of the spray are obtained from unsteady in-nozzleflow simulations of a two-hole real size injection nozzle.The simulation approach comprehend the unsteady simulationof the nozzle flow, recording the spatial distribution of the flowproperties (�v, ρ, k, ε) at the nozzle exit as a function of time,both for Diesel fuel and Diesel vapour. These properties arethen used as a boundary condition for the subsequent unsteadyLagrangian spray calculations, yielding initial conditions forthe spray velocities, injected mass and available breakupenergy. The unsteady simulation of the nozzle flow was carriedout including the movement of the needle (injector opening).

This coupling method is convenient to deal with the at-

Figure 1: Simulation Approach

omization of non-axial symmetric liquid jets penetrating indense gaseous ambient with very high velocities like the onesencountered in high pressure Diesel injection. Under theseconditions a very fast disintegration of the coherent liquidflowing in the nozzle into drops of different sizes and shapescan be expected. This assumption of a very short intact corelength can be found quite often in the literature [14]. Thus, thepresent numerical transition of the Eulerian two-phase flow inthe nozzle into the Lagrangian two-phase particle flow in thechamber should offer a good approach to the problem.The performance of the primary breakup model is then evalu-ated by means of a comparison between the results of the spraysimulations and optical spray measurements, including spraypenetration Sp(t), near and far spray angles. All measurementswere carried out in the test facilities of Continental AutomotiveGmbH in Regensburg [9].

NOZZLE FLOW SIMULATION SETUP

The primary breakup model uses detailed information from3D turbulent cavitating nozzle flow simulations performed withthe Ansys CFX CFD code based on a Volume of Fluid (VOF)method [1]. This model was chosen because it offers a goodcompromise between computational effort and results quality.The VOF-model assumes that both gas and liquid phases sharethe same pressure and velocity. The two-phase flow is con-sidered homogeneous, isothermal and the liquid and vapourphases incompressible, having constant density values. Thecalculations are time-dependent because of the highly transientbehaviour of the nozzle flow, specially in the needle openingphase.The simplified Rayleigh-Plesset model is employed for the masstransfer term between phases. This model bases on the growthof a single spherical bubble in an unbounded liquid domain [4].The SST shear stress transport turbulence model is employedin the simulations [1], assuming the flow to be fully turbulent.Fluid temperature is assumed to be constant in the whole do-main and the energy equation is not solved.For the nozzle simulations meshes of about 106 cells were used,paying special attention on the resolution of the boundary layerwith 8-10 nodes. The movement of the needle is simulated withthe Displacement Diffusion model [1]. With this model, the dis-placement applied on the needle is diffused to other mesh pointsby solving the equation:

∇ · (Γdisp∇δ) = 0 (1)

In this equation, δ is the displacement relative to the previousmesh locations and Γdisp is the mesh stiffness, which deter-mines the degree to which regions of nodes move together.Figure 2 shows the geometry of one of the injection holes of thestudied nozzle. Both holes have different values of included an-gle, that is the angle included between the injector axis and theinjection hole axis. Higher included angles show higher ten-dencies to cavitate and to produce an asymmetric flow insidethe hole. The important geometrical parameters for this paperare listed on Table 2. Here, CF (conicity factor) and HE (inletrounding) are typical geometrical parameters of Diesel injectionnozzles [9], where

CF =Din − Dout

Lhole· 100 (2)

Low values of CF and HE cause high curvature of the stream-lines, promoting cavitation.

The duration of the simulations equals the typical injectiontime tinj of 1ms using a timestep of ∆t = 1.5 · 10−6s. Therest of the boundary conditions of the problem are summarisedin Table 1. The operating points were chosen in order toappreciate the influence of both back (pgeg) and injectionpressures (pvor) on the calculated sprays.

VALIDATION OF NOZZLE FLOW

As a first step, the simulations of the cavitating flow are val-idated by comparing hydraulic flow measurements of the noz-zles with the computed values. The measured hydraulic proper-ties of the nozzle are the hydraulic flow, the characteristic curveand the critical cavitation point CCP, which are defined in thenext paragraphs.

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Figure 2: Scheme of nozze tip. Geometrical parameters

Case pvor pgeg

1 800 202 1300 203 1600 104 1600 205 1600 40

Table 1: Operating points for experiments and simulations

Inj. Hole HE(µm) HW (◦) CF (−)1 11 72 0.6752 11 88 0.6

Table 2: Geometrical parameters of the studied nozzles

The nozzle hydraulic flow is the measured Diesel flow througha nozzle for a pressure difference of 100 bar. For a better eval-uation of these results, the hydraulic flow of the nozzle is cal-culated under ideal conditions (Bernouilli equation) so that theefficiency of the nozzle can be described with a single parameter

η =HD

HDber(3)

Hydraulic flow simulations show a good agreement, for theuncertainty of the hydraulic flow test bench is of about 3%.The characteristic curve of the nozzle in Fig. 3 shows the

HDber HDexp ηexp HDsim ηsim

5.86 · 10−3 4.32 · 10−3 0.738 4.37 · 10−3 0.746

Table 3: Hydraulic flow in l/s and efficiency of the studiednozzles

massflow of the nozzle for different needle lifts, under a drivingpressure difference of ∆p = 100 bar. It can be seen that thecalculated hydraulic flow agrees quite well with the measuredone. It is important to note that the nozzle reaches its nominalhydraulic flow for needle lifts higher than 50-60 µm. For lowerlifts, the flow is determined by the gap between the needle andthe seat area of the needle. It rises with the needle until themain throttle is shifted to the injection hole. This behaviour iswell reproduced by the simulations.For the characterisation of the cavitating conditions of the flow

Figure 3: Characteristic curve of the investigated nozzle.Experiment and simulation.

the critical cavitation point CCP is of great help. The CCP is anon-destructive hydraulic measurement accounting for the re-lation of inj. pressure to back pressure for the onset of “chokedflow” [9, 6]. To obtain this point, several measurements ofthe hydraulic flow are carried out for a constant injectionpressure of pvor = 100 bar while decreasing the back pressurefrom pgeg = 100 bar to pgeg = 1 bar. As seen in Figure 4,the simulated hydraulic flow of the nozzle increases with thepressure difference and the nozzle begins to cavitate so that apart of the flow cross section is filled with vapour. At a certainpoint the nozzle delivers a more or less constant hydraulic floweven if the pressure difference is raised. The point where thenozzle is “choked” because of cavitation is well reproduced bythe simulation.

It is important to mention that turbulence was assumed to

Figure 4: Determination of the CCP. Experiment andsimulation.

be fully developed for all calculations. This is probably nottrue because of the length of the nozzle, which is not enoughfor turbulence to develop. From this point of view, the flowinstabilities are overestimated by the calculations. At the sametime, the collapse and detachment of vapour cavities inside theinjection hole, which cause instabilities in the flow and promotethe breakup, can’t be calculated with the chosen mathematicalapproach. From this other point of view, the instabilities whichpromote breakup will be underestimated. It is assumed for thiswork that both effects are balanced and the general level ofinstabilities is well estimated.After assuring the reliability of the simulations setup of thenozzle, unsteady simulations were carried out for the boundary

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conditions shown in Table 1. The variables which play a rolefor the subsequent breakup of the liquid (�v, ρ, k, ε) are thenrecorded as a function of time and space to be used as initialconditions by the primary breakup model.

PRIMARY BREAKUP MODEL

Based on the results of a detailed investigation of the flowinside the injection holes of high pressure Diesel injectors [5], amodel for cavitation and turbulence induced primary break-upof liquid jets was developed some years ago [3]. The model usesa cavitation and turbulent energy based approach for the evalu-ation of all necessary starting conditions for the calculation ofsecondary break-up like drop sizes, velocity components andspray angle. This model has been now enhanced to be appliedfor 3D nozzle flow simulations accounting not only for turbu-lence and cavitation intensities inside the injection hole, but alsofor the velocity distribution at the hole exit.The break-up energy is estimated by means of a two-phase flowsimulation of the nozzle, as explained above. After that, an en-ergy balance is drawn in order to calculate the properties of theprimary injected droplets. The probability for new particles tobe created at a certain position of the nozzle exit depends on thespatial resolution of the mass flow at the nozzle exit, so that ahigher mass flow is represented by a higher number of particles.The spray angle is given by the diverging velocities describedin the initial droplet velocity vectors �v. With this coupled ap-proach, no initial value from empiric correlations needs to beused in the simulation chain and asymmetries of the nozzle floware reproduced in the spray.The break-up energy consists of the two following terms: flow-induced turbulent kinetic energy Eturb [3, 2] and cavitation in-duced turbulent kinetic energy Ecav [17, 3, 11]. Turbulent fluc-tuations acting on the surface of a jet cause instabilities whichlead to break-up. The same approach is used when consider-ing the instabilities caused when modeling the released energyof collapsing cavitation bubbles: only the induced instabilitiesnear the surface are assumed to contribute to the break-up. Flowinduced turbulent kinetic energy is a direct output of nozzle flowsimulation, while cavitation induced turbulent kinetic energyhas to be calculated by resolving the cavitation bubble dynam-ics [3].As a first step, the flow at the nozzle exit is divided in twozones depending on the liquid and gas contents. Cells with avolume fraction of vapour V F > 0.1 belong to the cavitatingzone (zone 2) and the rest to the liquid zone (zone 1), as seenin figure 5. Then, a cylindrical control volume for the energybalance is defined, where the length is equal to the effective di-ameter deff of the liquid zone. After that, the break-up energyis evaluated for each zone as follows:

Ei = ηi · (Ecav,i + Ekin,turb,i) (4)

Here, i=zone 1 or zone 2 and η represent the efficiency of theenergy transformation, and has a value of 1 for this first evalua-tion of the model.It is assumed that the total break-up energy in zone 2 turns into

surface energy for the formation of n2 droplets and for theirradial kinetic energy.

E2,eff = Eσ2 + Ekin2 (5)

Eσ2 = σ · πd2cav · n2 (6)

Figure 5: Typical distribution of zones at the nozzle exit

Ekin2 =12· v2

r2 · mdroplet · n2 (7)

n2 =6 · m2

π · d3cav · ρl

(8)

For the liquid zone it is assumed that the total energy is presentas turbulent fluctuations that act against the stabilizing surfaceforces [3, 11]. Mass is split off the liquid zone until both forcesare in equilibrium:

Uturb =√

2 · E1

3 · m1(9)

Fturb =12ρL · u2

turb · S (10)

Fσ = 2 · σ · (2 · deff ) (11)

C · Fturb = Fσ (12)

Here, S is the surface of the liquid where the turbulent disrupt-ing force is acting and deff the effective diameter of zone 1. Inorder to obtain plausible values for the diameter of the injecteddroplets it is necessary to multiply the disrupting force by a co-efficient C = O(10−2) [2].The remaining mass is transformed to a cylindrical droplet ofdiameter drem,cyl, and its energy content is used to calculate itsradial velocity.

drem,cyl =2 · σ · S/deff

S/deff ·ρL·E13m1

− 2σ(13)

The cylindrical droplet is then turned into a spherical one:

drem = 3

√32· d2

rem,cyl · S/deff (14)

The split mass undergoes then the same calculation of eq 5 toeq 7 in order to obtain droplets of size dspl.

SPRAY SIMULATION SETUP

For the description of the spray penetrating the dense gasambient two phases are considered: the dispersed phase (fluiddroplets) and the gas phase (continuum). The gas phase is mod-eled with the Eulerian approach using the Navier Stokes equa-tions, while the dispersed phase is tracked through the flow ina Lagrangian way. The tracking is carried out by forming a setof ordinary differential equations in time for each particle, con-sisting of equations for position and velocity [15].

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Since the concentration of the droplets in the fluid stream ishigh, two-way coupling is considered between the phases. Thisimplies that the fluid affects the particle motion through the vis-cous drag and a difference in velocity between the particle andfluid, and conversely, there is a counteracting influence of theparticle on the fluid flow due to the viscous drag. Droplet colli-sion and coalescence are not considered. In addition to the dragforces, turbulent dispersion is also taken into account for thesesimulations. Although the gas-phase turbulence induced by thishigh-pressure-driven spray is anisotropic [12], an isotropic dis-persion approach with the k−ε model is used. The initial turbu-lence levels are very low (k = 1e−4 and µturb = 0.1). For thesecondary breakup, the Cascade Atomization Breakup model(CAB) was used [16] due to its good performance for high pres-sure Diesel sprays [10]. This model allows droplets to deform,so that a modification of the drag coefficient due to the variationof the droplet cross section is needed. The particle source termsare generated for each particle as they are tracked through theflow. Particle sources are applied in the control volume that theparticle is in during the time step.It is well known that the mesh can play an important role whensimulating sprays with the Lagrangian approach. For this workan adaptive mesh was used (Fig. 6), so that for the perpendic-ular directions, the used lengths of a computational cell for thecalculations are about 0.15 mm. in the dense spray zone and 0.8mm. for far field of the spray. In the axial direction, an almostconstant cell length of 0.8 mm. was used. The domain has a to-tal length of 10 cm. in the axial direction and 2 cm. in the othertwo perpendicular directions., which results in a total number ofcells of about 105. For all calculations a parcel injection rate of2 · 108 parcels per second was taken, which should be enoughto deliver statistical convergence for the calculation.

Figure 6: Mesh

VALIDATION OF SPRAY CALCULATIONS

Taking into account the limitations and sensitivities of theLagrangian approach, the calculations are now compared tomeasurements. Due to the limited extension of this paper, theevaluation of the model performance will be carried out bymeans of the comparison of the sprays produced by only theinjection hole 1, which is defined on Table 2. Due to the lowvalues of HE and CF, cavitation and high turbulence values areexpected, and confirmed with the validation of the nozzle flow(Fig. 4).The spray visualization was performed using a CCD Cameraand a backlight [9]. Spray penetration and both near andfar spray angles were obtained as a function of time for theinvestigated sprays. The definition of the far spray angle andpenetration can be obtained from Figure 7, where the mass of

the spray is divided into three zones, containing 20%, 50% and99% of the spray mass. The near field spray angle is defined

Figure 7: Definition of spray parameters

as the angle between the spray contour for 20% of the spraymass and the point of intersection between the injection holeaxis and the injector axis.In Figure 8a the influence of the injection pressure on thespray penetration is represented. As expected, higher pressuredifferences lead to a higher spray impulse, resulting in higherpenetration. This tendency can be observed in the diagram,both for the computed and measured sprays. The agreementbetween experiments and simulations is good for the first halfof the injection, which confirms that the nozzle simulationsyield correct initial impulse conditions. For the second half ofthe injection, the penetration is underestimated due to both thelack of coalescence model in the CFD code and to the meshsensitivity of the Lagrangian approach. The coalescence modelin dense sprays would cause “old” slow droplets in spray tointeract with “new” droplets, leading to higher droplet sizes andvelocities which could penetrate further. The second reasonis the mesh dependency of the Lagrangian approach: here thecode underestimates the momentum exchange between phasesso that the acceleration of the gas phase is lower than the realone and the spray is slowed down.In Figure 8c the development in time of the mean size of theinjected primary droplets, i.e. before secondary breakup, isrepresented together with the needle lift. For low needle lifts,the smallest flow cross section can be found in the needle seatarea, and the flow in the injection holes is slow, not cavitatingand laminar. Under these conditions, the available breakupenergy is very low and therefore the injected droplets are big,of the size of the hole diameter. This corresponds to the wellknown and widely used “blob method” of Reitz et al. for theprimary breakup [13]. If the needle continues to open, the flowis not restricted anymore in the needle seat area causing anacceleration of the flow in the injection hole. This results inan increase of available breakup energy, present in the flow ascavitating and turbulent instabilities, so that the model yieldssmaller droplets. These two Figures 8a and 8c show that thepresented primary breakup model can reproduce the effect of avariation of the inj. pressure on the spray penetration and thedroplet size distribution. As expected and often shown in theliterature, in the case of a higher injection pressure the meansize of the droplets is smaller and the spray penetrates further,although the curves in the case of penetration show almostthe same values. There are two counteracting effects on thepenetration length when increasing the injection pressure. Onone hand the impulse of the flow leaving the nozzle is higher,

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(a) Spray penetration for different injection pressures (b) Spray penetration for different back pressures

(c) Mean primary droplet sizes and needle lift. Variation of injection pressure (d) Mean primary droplet sizes and needle lift. Variation of back pressure

(e) Influence of back pressure on near spray angles (f) Influence of back pressure on far spray angles

Figure 8: Simulation vs. experimental results

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which leads to higher penetration, but on the other hand thedroplets are smaller so they break up faster and penetrate less.For this reason the penetration curves of both cases are verysimilar.The influence of the back (chamber) pressure is shown onFigure 8b. The higher density of the gas in the case of highpressures promotes the interaction between both phases, lead-ing to lower penetration values. In addition to that, the releasedenergy by the collapse of cavitation bubbles increases withhigh back pressures following the Rayleigh-Plesset equation[4]. Therefore the available breakup energy is higher for higherback pressures. This leads to a smaller mean droplet sizecalculated by the model for high back pressures, but only in thecase of cavitating nozzles, as seen in Fig. 8d. This is also inagreement with the reports found in the literature dealing withthe influence of the back pressure on the spray characteristics[14].According to the empirical correlations found in the literature,the effect of the back pressure on the penetration length isat least so important as the effect of the injection pressure[14]. For the presented model the back pressure seems to havea clearly more significant effect than the injection pressure,what can be appreciated by comparing the difference betweenthe calculated penetration lengths in Fig. 8a and 8b. Similarbehaviour can be found when considering the mean dropletsize of Figures 8c and 8d. Most of the empirical correlationsfor the droplet size distribution of the spray assume a similareffect of both injection and back pressures. The results of thesimulation show a much higher effect of the injection pressureon the droplet size distribution. Here, it has to be consideredthat the empirical correlations were obtained considering bothprimary and secondary droplets and the diagrams of Figures 8cand 8d show only the mean size of the primary droplets, wherereliable experimental data are very rare.Figure 8e and 8f show the calculated near and far spray anglesof the investigated nozzle compared to the measurements.The diagrams show also the influence of the back pressure onthe development of the spray. The influence of the injectionpressure is not represented because it does not play a role onthe development of the spray angles, as derived from severalempirical correlations developed for Diesel injection found inthe literature [14, 13]. Both measurements and simulationsshow higher values in the case of high back pressures forboth far and near angles. There are two main reasons for thisbehaviour: On the one hand, a bigger divergence of the dropletscan be expected for higher back pressures due to the strongerinteraction between gas and liquid. On the other hand, thereleased energy from bubble collapse depends on the backpressure, influencing the cavitation induced breakup energy,so that high energy levels lead to high radial velocities ofthe created droplets. Both effects influence the measured andcalculated spray angles, as seen in Fig 8e-8f. The agreementbetween experiments and calculations is quite good for the nearspray angles and reasonably good in the case of the far sprayangles. Nevertheless, tendencies are well reproduced in bothcases. This disagreement is due to the different division of thespray in three parts depending on the mass content (see Fig.7)for simulations and experiments, since in the latter case thisinformation is obteined from a 2D picture, leading to slightlydifferent results.The diagrams of figures 8c and 8d show the mean size of the

300 parcels injected in the domain in every timestep. These

Figure 9: Primary Droplet Distribution for two different backpressures

values are calculated by the primary breakup model. Themodel calculates three different primary droplet sizes for everytimestep depending on the origin of the breakup energy, drem,dspl, dcav. For a better description of the performance of themodel, figure 9 shows a histogram of the frequency of thecalculated sizes. As explained above, the size of the primarydroplets for high chamber pressures is small because of thehigher available breakup energies. In the histogram there isa shift to the left (lower sizes) for each of the three primarydroplet types when increasing back pressure, following thetrends found in experimental works [14]. On top of that, thecalculated sizes for dcav, which are the droplets to be foundon the spray contour, are in very good agreement with themeasured values by [8]. Droplets which are responsible of thefar characteristics of the spray and correspond to the spraycore (drem, dspl) show sizes of about 30%-70% of the nozzlediameter, which are also plausible values for a cavitating nozzleunder fully open needle conditions.

CONCLUSIONS

This paper has been focused on high-pressure-drivenDiesel fuel spray simulation and a primary breakup model hasbeen evaluated by means of optical measurements of a spray.In order to take into account the flow conditions inside thenozzle on liquid jet breakup, a coupled approach has been used,including unsteady two phase 3D simulations of both nozzleflow and spray.Unsteady nozzle flow simulations including opening injectorneedle have been carried out and compared with hydraulicmeasurements with satisfactory results.Regarding the spray, the comparison between numerical resultsand experiments has shown the reasonably good performanceof the presented model in predicting the primary breakup pro-cess, taking into account the shortcomings of the Lagrangianapproach for the simulation of such two phase flows. In the areanear the nozzle exit, right after the primary breakup takes place,measurements and simulations show a very good agreement.The initial penetration of the Diesel spray and its near angle arewell predicted. On the contrary, penetration and spray angle ofthe spray in the far field of the nozzle show less good agreementdue to the known mesh dependency of the Lagrangian approachand to the lack of coalescence model. It is important to note thateven if the quantitative results are not as good as expected, thequalitative evaluation of the model predicts the right tendencies.Better quantitative results could be achieved with a lower value

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of the constant C (Eq. 12), which would lead to bigger primarydroplets and higher penetration.These results, and others which will be published in the nearfuture, show that the presented primary breakup model is avery good starting point in order to understand and describe theinfluence of the nozzle flow on the primary breakup. On theother hand, this investigation also showed the suitability of theLagrangian approach for the simulation of the thin spray, whilean Eulerian approach could be more efficient for the calculationof dense sprays.

NOMENCLATURE

Symbol Quantity UnitCCP Critical Cavitation Point barCF Conicity Factor -d Droplet Diameters mD Nozzle Diameters mE Energy Kg · m2/s2

L Length mm Mass KgHD Hydraulic Flow l/sHE Inlet Rounding mp Pressure barSp Penetration mt Time sVF Volume Fraction -

Greek LettersΓdisp Mesh Stiffness N/mδ Nodes displacement mη Efficiency -σ Surface Tension N/mµ Dynamic Viscosity Kg/m · s

Subscripts1 Liquid Zone2 Cavitation Zoneber Bernouillicav Cavitationeff Effectiveexp Experimentgeg After Nozzlein Inletinj Injectionkin KineticL Liquidout Outletr Radialrem Remaining Masssim Simulationspl Split Massturb Turbulencevor Before Nozze

References[1] ANSYS CFX-Solver Theory Guide. Ansys Europe, Ltd.,

2006.

[2] C. Arcoumanis and M. Gavaises. Linking nozzle flow withspray characteristics in a diesel fuel injection system. At-omization and Sprays, 8:307–347, 1998.

[3] C. Baumgarten. Modellierung des Kavitationsein-

flusses auf den primären Strahlzerfall bei der Hochdruck-Dieseleinspritzung. PhD thesis, University Hannover,2003.

[4] C.E. Brennen. Cavitation and Bubble Dynamics. ISBN0-19-509409. Oxford University Press, 1995.

[5] R. Busch. Untersuchung von Kavitationsphänomenen inDieseleinspritzdüsen. PhD thesis, University Hannover,2001.

[6] H. Chaves, M. Knapp, A. Kubitzek, F. Obermeier, andT. Schneider. Experimental study of cavitation in the noz-zle hole of diesel injectors using transparent nozzles. SAE,(SAE 950290), 1995.

[7] N. Chigier and R.D. Reitz. Regimes of jet breakup andbreakup mechanisms (physical aspects). Recent Advancesin Spray Combustion: Spray Atomization and Drop Burn-ing Phenomena, 1, 1996.

[8] A. Fath. Charakterisierung des Strahlaufbruch-Prozessesbei der instationären Druckzerstäubung. PhD thesis, Uni-versität Erlangen-Nürnberg, 1997.

[9] E. Kull. Einfluss der Geometrie des Spritzlochs von Diese-leinspritzdüsen auf das Einspritzverhalten. PhD thesis,Universität Erlangen-Nürnberg, 2003.

[10] E. Kumzerova. Validation of spray simulations in cfx-11.Ansys CFX Internal Validation Report, 2006.

[11] A. Nishimura and D.N. Assanis. A model for primarydiesel fuel atomization based on cavitation bubble collapseenergy. Institute for Liquid Atomization and Spray Sys-tems, 2000.

[12] P. Pelloni and G.M. Bianchi. A cavitation-induced atom-ization model for high-preesure diesel spray simulations.32 ISATA International Congress, (99SIO44), 1999.

[13] R.D. Reitz and F.V. Bracco. Mechanisms of atomizationof a liquid jet. Phys. Fluids, 1982.

[14] B.M. Schneider. Experimentelle Untersuchungen zurSpraystruktur in transienten, verdampfenden und nichtverdampfenden Brennstroffstrahlen unter Hochdruck.PhD thesis, Eidgenössischen Technischen HochschuleZürich, 2003.

[15] M. Sommerfeld. Modellierung und numerische Berech-nung von Partikelbeladenen Strömungen mit Hilfe desEuler/Lagrange-Verfahrens. Shaker Verlag, Aachen,1996.

[16] F.X. Tanner. A cascade atomization and drop breakupmodel for the simulation of high-pressure liquid jets. SAE,(2003-01-1044), 2003.

[17] E. von Berg, A. Alajbegovic, D. Greif, A. Poredos,R. Tatschl, E. Winklhofer, and L.C. Ganippa. Primarybreak-up model for diesel jets based on locally resolvedflow field in the injection hole. Institute for Liquid Atom-ization and Spray Systems, 2002.

[18] E. von Berg, W. Edelbauer, A. Alajbegovic, R. Tatschl,M. Volmajer, B. Kegl, and L.C. Ganippa. Coupled simu-lations of nozzle flow, primary fuel jet breakup, and sprayformation. Journal of Engineering for Gas Turbines andPower, Vol 127:897, 2005.

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